On the unimodality of independence polynomials of some graphs

Abstract

In this paper we study unimodality problems for the independence polynomial of a graph, including unimodality, log-concavity and reality of zeros. We establish recurrence relations and give factorizations of independence polynomials for certain classes of graphs. As applications we settle some unimodality conjectures and problems.

arXiv comment17 pages, to appear in European Journal of Combinatorics

References in corpus (4)

• A unified approach to polynomial sequences with only real zeros
• Log-concavity and LC-positivity
• On linear transformations preserving the Pólya Frequency property
• Very well-covered graphs with log-concave independence polynomials

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• On trees with real rooted independence polynomial
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• Operations of graphs and unimodality of independence polynomials
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• 1-well-covered graphs revisited
• Unimodality of the independence polynomials of non-regular caterpillars
• Recurrence Relations for Graph Polynomials on Bi-iterative Families of Graphs
• Analytic properties of sextet polynomials of hexagonal systems
• On Unimodality of Independence Polynomials of Trees